Connectivity-preserving formation stabilization of unicycles in local coordinates using minimum spanning tree

In this paper, we present a novel formation control method to stabilize the positions of a multiagent team moving in a two-dimensional environment to a specified rigid pattern. Agent interactions are typically range-constrained in this kind of system, which makes it critical to maintain the connectivity of the underlying network formed by the mobile agents to enable completion of the desired task. To address this issue, we study the problem of connectivity preservation coupled with the formation control objective. Our contribution is a globally stable formation stabilization approach that maintains connectivity and is designed for unicycle kinematics. Each agent computes its motion using the relative positions of the other agents, expressed in its local arbitrarily oriented coordinate frame. To preserve connectivity, our method relies on a procedure where the desired formation is adaptively scaled to ensure maintenance of the links in the Minimum-distance Spanning Tree of the communications graph. This way, instead of requiring additional control components for connectivity management which may interfere with the formation control objective, we integrate the two goals in the same, bounded, control input. We show formally that the controller provides global stability and ensures connectivity maintenance, and we illustrate its performance in simulation.